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The Pauli exclusion principle helps explain a wide variety of physical phenomena. One particularly important consequence of the principle is the elaborate electron shell structure of atoms and the way atoms share electrons, explaining the variety of chemical elements and their chemical combinations.
Pauli formulated his exclusion principle, stating, "There cannot exist an atom in such a quantum state that two electrons within [it] have the same set of quantum numbers." [39] A year later, Uhlenbeck and Goudsmit identified Pauli's new degree of freedom with the property called spin whose effects were observed in the Stern–Gerlach experiment.
The Pauli exclusion principle states that only one fermion can occupy any such sublevel. The number of ways of distributing n i indistinguishable particles among the g i sublevels of an energy level, with a maximum of one particle per sublevel, is given by the binomial coefficient, using its combinatorial interpretation: (,) =!!
Multiple bosons may occupy the same quantum state; however, by the Pauli exclusion principle, no two fermions can occupy the same state. Since electrons have spin 1/2, they are fermions. This means that the overall wave function of a system must be antisymmetric when two electrons are exchanged, i.e. interchanged with respect to both spatial ...
The analog formula to the above generalization of Euler's formula for Pauli matrices, the group element in terms of spin matrices, is tractable, but less simple. [ 7 ] Also useful in the quantum mechanics of multiparticle systems, the general Pauli group G n is defined to consist of all n -fold tensor products of Pauli matrices.
These "new" states could violate the Pauli exclusion principle. The aim of VIP2 is to search for new quantum states, which have a symmetric component in an otherwise antisymmetric state. These non-Paulian states can be identified by the characteristic X-rays emitted during Pauli exclusion principle—prohibited atomic transitions to the ground ...
Degenerate matter occurs when the Pauli exclusion principle significantly alters a state of matter at low temperature. The term is used in astrophysics to refer to dense stellar objects such as white dwarfs and neutron stars, where thermal pressure alone is not enough to prevent gravitational collapse.
We need to consider only the outer 3p 2 electrons, for which it can be shown (see term symbols) that the possible terms allowed by the Pauli exclusion principle are 1 D , 3 P , and 1 S. Hund's first rule now states that the ground state term is 3 P, which has S = 1. The superscript 3 is the value of the multiplicity = 2S + 1 = 3.